We examine the 2008-2016 $gamma$-ray and optical light curves of three bright BL Lac objects, 0716+714, MRK 421, BL Lac, which exhibit large structured variability. We searched for periodicities by using a fully Bayesian approach. For two out of three sources investigated no significant periodic variability was found. In the case of BL Lac we detected a periodicity of ~ 680 days. Although the signal related to this is modest, the coincidence of the periods in both gamma and optical bands is indicative of a physical relevance. Considering previous literature results, possibly related $gamma$-ray and optical periodicities of about one year time scale are proposed in 4 bright $gamma$-ray blazars out of the 10 examined in detail. Comparing with results from periodicity search of optical archives of quasars, the presence of quasi-periodicities in blazars might be more frequent by a large factor. This suggests the intriguing possibility that the basic conditions for their observability are related to the relativistic jet in the observer direction, but the overall picture remains uncertain.
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